Problem with mechanical Rigging
Maybe you don't tell enough. But if you want to only move the left big bone (bone1) so that the other ones follow you could use this setup:


Give bone1 a Limit Rotation constraint so that it stays on its axis.
Give bone2 a Copy Rotation so that it copies bone1's rotation.
Give bone3 a Track To so that it keeps pointing at the tail fo bone2.
Give bone4 a Copy Rotation so that it copies bone3 rotation.